## Quick Reference

Random variables *X*_{1}, *X*_{2},…, *X** _{n}* (each with ranges from−∞ to ∞) have a multivariate normal distribution if their joint probability density function f is given by where

**x**is the

*n*×1 vector of values,

*μ*is the

*n*×1 vector of means,

**Σ**is the

*n*×

*n*variance–covariance matrix, and det(

**Σ**) is the determinant of

**Σ**.

For the special case of the bivariate normal distribution, with random variables *X* and *Y*, the joint probability density function f is given by where the mean and variance of *X* are *μ** _{x}* and

*σ*

^{2}

_{x}, the mean and variance of

*Y*are

*μ*

*and*

_{y}*σ*

_{y}^{2}, and

*ρ*is the correlation coefficient between the two variables.

*Subjects:*
Probability and Statistics.

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